x = 7.5 and y = 75°
Explanation:
ΔMNO is an equilateral triangle
So, all the interior angles, ∠MNO, ∠NOM and ∠NMO are same
∠MNO + ∠NOM + ∠NMO = 180°
z + z + z = 180°
3z = 180°
z = 60°
Thus, ∠MNO , ∠NOM and ∠NMO = 60°
∠MNO = 2x + 4x + 2x
60° = 8x
x = 7.5
In ΔNOB,
∠BNO + ∠NOB + ∠OBN = 180°
2x + 60° + ∠OBN = 180°
15° + 60° + ∠OBN = 180°
∠OBN = 105°
∠NBA = 180° - ∠OBN
y = 180° - 105°
y = 75°
Therefore, x = 7.5 and y = 75°
